Difference between revisions of "ApCoCoA-1:CharP.IMNLASolve"

From ApCoCoAWiki
(New page: <command> <title>CharP.GBasisF2</title> <short_description>Computing the unique <tt>F_2-</tt>rational zero of a given polynomial system over <tt>F_2</tt>.</short_description> <synt...)
 
Line 3: Line 3:
 
     <short_description>Computing the unique <tt>F_2-</tt>rational zero of a given polynomial system over <tt>F_2</tt>.</short_description>
 
     <short_description>Computing the unique <tt>F_2-</tt>rational zero of a given polynomial system over <tt>F_2</tt>.</short_description>
 
<syntax>
 
<syntax>
CharP.MNLASolve(F:LIST):LIST
+
CharP.IMNLASolve(F:LIST):LIST
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
Line 9: Line 9:
  
 
<par/>
 
<par/>
This function computes the unique zero in <tt>F_2^n</tt> of a polynomial system over <tt>F_2 </tt>. It uses Mutant NLA<tt>-</tt>Algorithm to find the unique zero. The Mutant NLA<tt>-</tt>Algorithm generates a sequence of linear systems to solve the given system. The Mutant NLA<tt>-</tt>Algorithm can find the unique zero only. If the given polynomial system has more than one zeros in <tt>F_2^n </tt> then this function does not find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound. In fact Mutant NLA<tt>-</tt>Algorithm is the NLA<tt>-</tt>Algorithm with mutant strategy. It uses <ref>linalg.EF</ref> for gaussian elimination.
+
This function computes the unique zero in <tt>F_2^n</tt> of a polynomial system over <tt>F_2 </tt>. It uses Improved Mutant NLA<tt>-</tt>Algorithm to find the unique zero. The Improved Mutant NLA<tt>-</tt>Algorithm generates a sequence of linear systems to solve the given system. The Improved Mutant NLA<tt>-</tt>Algorithm can find the unique zero only. If the given polynomial system has more than one zeros in <tt>F_2^n </tt> then this function does not find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound. In fact Improved Mutant NLA<tt>-</tt>Algorithm is the NLA<tt>-</tt>Algorithm with improved mutant strategy. It uses <ref>linalg.EF</ref> for gaussian elimination.
  
  
Line 29: Line 29:
  
 
-- Then we compute the solution with
 
-- Then we compute the solution with
CharP.MNLASolve(F);
+
CharP.IMNLASolve(F);
  
 
-- And we achieve the following information on the screen together with the solution at the end.
 
-- And we achieve the following information on the screen together with the solution at the end.
 
----------------------------------------
 
----------------------------------------
   
+
      Finding Variable: x[4]
Finding Variable: x[4]
 
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=4
 
No. of Rows=4
Line 41: Line 40:
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=4
 
No. of Rows=4
Line 48: Line 47:
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=11
 
No. of Rows=11
Line 63: Line 62:
 
-------------------------------
 
-------------------------------
 
Gaussian Elimination Completed.
 
Gaussian Elimination Completed.
The No. of Mutants found = 0
+
No. of New Mutants found = 0
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=8
 
No. of Rows=8
Line 70: Line 69:
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=11
 
No. of Rows=11
 
No. of Columns=8
 
No. of Columns=8
 
Appling Gaussian Elimination to check solution coordinate...
 
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0.015
+
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
 
Gaussian Elimination Completed.
 
Gaussian Elimination Completed.
Line 85: Line 84:
 
-------------------------------
 
-------------------------------
 
Gaussian Elimination Completed.
 
Gaussian Elimination Completed.
The No. of Mutants found = 1
+
No. of New Mutants found = 1
 +
The total No. of Mutants found are = 1
 +
The No. of Mutants of Minimum degree (Mutants used) are = 1
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=11
 
No. of Rows=11
 
No. of Columns=11
 
No. of Columns=11
 
Appling Gaussian Elimination for finding Mutants...
 
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0.016
+
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=11
 
No. of Rows=11
Line 115: Line 116:
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=4
 
No. of Rows=4
Line 122: Line 123:
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=7
 
No. of Rows=7
Line 137: Line 138:
 
-------------------------------
 
-------------------------------
 
Gaussian Elimination Completed.
 
Gaussian Elimination Completed.
The No. of Mutants found = 0
+
No. of New Mutants found = 0
 +
The size of Matrix is:
 +
No. of Rows=4
 +
No. of Columns=7
 +
Appling Gaussian Elimination for finding Mutants...
 +
-- CoCoAServer: computing Cpu Time = 0
 +
-------------------------------
 +
Gaussian Elimination Compeleted.
 +
The size of Matrix is:
 +
No. of Rows=7
 +
No. of Columns=5
 +
Appling Gaussian Elimination to check solution coordinate...
 +
-- CoCoAServer: computing Cpu Time = 0
 +
-------------------------------
 +
Gaussian Elimination Completed.
 +
The size of Matrix is:
 +
No. of Rows=7
 +
No. of Columns=5
 +
Appling Gaussian Elimination to check solution coordinate...
 +
-- CoCoAServer: computing Cpu Time = 0
 +
-------------------------------
 +
Gaussian Elimination Completed.
 +
No. of New Mutants found = 0
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=7
 
No. of Rows=7
Line 144: Line 167:
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=7
 
No. of Rows=7
Line 160: Line 183:
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=3
 
No. of Rows=3
Line 167: Line 190:
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=4
 
No. of Rows=4
Line 183: Line 206:
 
Gaussian Elimination Completed.
 
Gaussian Elimination Completed.
 
x[2] = 1
 
x[2] = 1
[0, 1, 0, 1]
+
[0, 1, 0, 1]  
 +
 
  
 
</example>
 
</example>
Line 200: Line 224:
  
 
-- Then we compute the solution with
 
-- Then we compute the solution with
CharP.MNLASolve(F);
+
CharP.IMNLASolve(F);
  
 
-- And we achieve the following information on the screen.
 
-- And we achieve the following information on the screen.
 
----------------------------------------
 
----------------------------------------
      
+
     Finding Variable: x[4]
Finding Variable: x[4]
 
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=4
 
No. of Rows=4
Line 212: Line 235:
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=3
 
No. of Rows=3
Line 219: Line 242:
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=9
 
No. of Rows=9
Line 234: Line 257:
 
-------------------------------
 
-------------------------------
 
Gaussian Elimination Completed.
 
Gaussian Elimination Completed.
The No. of Mutants found = 0
+
No. of New Mutants found = 0
 
The size of Matrix is:
 
The size of Matrix is:
No. of Rows=15
+
No. of Rows=7
 
No. of Columns=14
 
No. of Columns=14
 
Appling Gaussian Elimination for finding Mutants...
 
Appling Gaussian Elimination for finding Mutants...
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=14
 
No. of Rows=14
No. of Columns=12
+
No. of Columns=8
 
Appling Gaussian Elimination to check solution coordinate...
 
Appling Gaussian Elimination to check solution coordinate...
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
Line 251: Line 274:
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=14
 
No. of Rows=14
No. of Columns=12
+
No. of Columns=8
 
Appling Gaussian Elimination to check solution coordinate...
 
Appling Gaussian Elimination to check solution coordinate...
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
 
Gaussian Elimination Completed.
 
Gaussian Elimination Completed.
The No. of Mutants found = 4
+
No. of New Mutants found = 2
 +
The total No. of Mutants found are = 2
 +
The No. of Mutants of Minimum degree (Mutants used) are = 2
 
The size of Matrix is:
 
The size of Matrix is:
No. of Rows=27
+
No. of Rows=9
No. of Columns=14
+
No. of Columns=10
 
Appling Gaussian Elimination for finding Mutants...
 
Appling Gaussian Elimination for finding Mutants...
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
No. of Rows=14
+
No. of Rows=10
No. of Columns=13
+
No. of Columns=8
 
Appling Gaussian Elimination to check solution coordinate...
 
Appling Gaussian Elimination to check solution coordinate...
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
Line 272: Line 297:
 
Gaussian Elimination Completed.
 
Gaussian Elimination Completed.
 
The size of Matrix is:
 
The size of Matrix is:
No. of Rows=14
+
No. of Rows=10
No. of Columns=13
+
No. of Columns=8
 
Appling Gaussian Elimination to check solution coordinate...
 
Appling Gaussian Elimination to check solution coordinate...
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
 
Gaussian Elimination Completed.
 
Gaussian Elimination Completed.
The No. of Mutants found = 0
+
No. of New Mutants found = 0
 
The size of Matrix is:
 
The size of Matrix is:
No. of Rows=12
+
No. of Rows=7
No. of Columns=14
+
No. of Columns=10
 
Appling Gaussian Elimination for finding Mutants...
 
Appling Gaussian Elimination for finding Mutants...
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Compeleted
+
Gaussian Elimination Compeleted.
 
The size of Matrix is:
 
The size of Matrix is:
No. of Rows=14
+
No. of Rows=10
No. of Columns=13
+
No. of Columns=8
Appling Gaussian Elimination to check solution coordinate...
 
-- CoCoAServer: computing Cpu Time = 0.016
 
-------------------------------
 
Gaussian Elimination Completed.
 
The size of Matrix is:
 
No. of Rows=14
 
No. of Columns=13
 
 
Appling Gaussian Elimination to check solution coordinate...
 
Appling Gaussian Elimination to check solution coordinate...
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
 
Gaussian Elimination Completed.
 
Gaussian Elimination Completed.
The No. of Mutants found = 0
 
 
The size of Matrix is:
 
The size of Matrix is:
No. of Rows=19
+
No. of Rows=10
No. of Columns=15
+
No. of Columns=8
Appling Gaussian Elimination for finding Mutants...
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
Gaussian Elimination Compeleted
 
The size of Matrix is:
 
No. of Rows=15
 
No. of Columns=14
 
 
Appling Gaussian Elimination to check solution coordinate...
 
Appling Gaussian Elimination to check solution coordinate...
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
 
Gaussian Elimination Completed.
 
Gaussian Elimination Completed.
 +
No. of New Mutants found = 0
 
The size of Matrix is:
 
The size of Matrix is:
No. of Rows=15
+
No. of Rows=22
 
No. of Columns=14
 
No. of Columns=14
Appling Gaussian Elimination to check solution coordinate...
+
Appling Gaussian Elimination for finding Mutants...
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
-------------------------------
Gaussian Elimination Completed.
+
Gaussian Elimination Compeleted.
The No. of Mutants found = 0
 
 
The size of Matrix is:
 
The size of Matrix is:
 
No. of Rows=14
 
No. of Rows=14
No. of Columns=15
+
No. of Columns=13
Appling Gaussian Elimination for finding Mutants...
 
-- CoCoAServer: computing Cpu Time = 0
 
-------------------------------
 
Gaussian Elimination Compeleted
 
The size of Matrix is:
 
No. of Rows=15
 
No. of Columns=14
 
 
Appling Gaussian Elimination to check solution coordinate...
 
Appling Gaussian Elimination to check solution coordinate...
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
Line 338: Line 341:
 
Gaussian Elimination Completed.
 
Gaussian Elimination Completed.
 
The size of Matrix is:
 
The size of Matrix is:
No. of Rows=15
+
No. of Rows=14
No. of Columns=14
+
No. of Columns=13
 
Appling Gaussian Elimination to check solution coordinate...
 
Appling Gaussian Elimination to check solution coordinate...
 
-- CoCoAServer: computing Cpu Time = 0
 
-- CoCoAServer: computing Cpu Time = 0
Line 349: Line 352:
 
seem to have a unique solution or it has
 
seem to have a unique solution or it has
 
no solution over the finite field F2.
 
no solution over the finite field F2.
 
  
 
</example>
 
</example>
Line 362: Line 364:
 
     <see>CharP.XLSolve</see>
 
     <see>CharP.XLSolve</see>
 
     <see>CharP.IMXLSolve</see>
 
     <see>CharP.IMXLSolve</see>
     <see>CharP.IMNLASolve</see>
+
     <see>CharP.MNLASolve</see>
 
      
 
      
  

Revision as of 11:28, 7 December 2010

CharP.GBasisF2

Computing the unique F_2-rational zero of a given polynomial system over F_2.

Syntax

CharP.IMNLASolve(F:LIST):LIST

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.


This function computes the unique zero in F_2^n of a polynomial system over F_2 . It uses Improved Mutant NLA-Algorithm to find the unique zero. The Improved Mutant NLA-Algorithm generates a sequence of linear systems to solve the given system. The Improved Mutant NLA-Algorithm can find the unique zero only. If the given polynomial system has more than one zeros in F_2^n then this function does not find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound. In fact Improved Mutant NLA-Algorithm is the NLA-Algorithm with improved mutant strategy. It uses linalg.EF for gaussian elimination.


  • @param F: List of polynomials of given system.

  • @return The unique solution of the given system in F_2^n.

Example

Use Z/(2)[x[1..4]];
F:=[
    x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1, 
    x[1]x[2] + x[1]x[3] + x[1]x[4] + x[3]x[4] + x[2] + x[3] + 1, 
    x[1]x[2] + x[1]x[3] + x[2]x[3] + x[3]x[4] + x[1] + x[4] + 1, 
    x[1]x[3] + x[2]x[3] + x[1]x[4] + x[2]x[4] + 1
    ];


-- Then we compute the solution with
CharP.IMNLASolve(F);

-- And we achieve the following information on the screen together with the solution at the end.
----------------------------------------
      Finding Variable: x[4]
	The size of Matrix is:
		No. of Rows=4
		No. of Columns=11
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=4
		No. of Columns=11
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=11
		No. of Columns=5
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	The size of Matrix is:
		No. of Rows=11
		No. of Columns=5
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	No. of New Mutants found = 0
	The size of Matrix is:
		No. of Rows=8
		No. of Columns=11
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=11
		No. of Columns=8
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	The size of Matrix is:
		No. of Rows=11
		No. of Columns=8
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	No. of New Mutants found = 1
	The total No. of Mutants found are = 1
	The No. of Mutants of Minimum degree (Mutants used) are = 1
	The size of Matrix is:
		No. of Rows=11
		No. of Columns=11
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=11
		No. of Columns=10
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	The size of Matrix is:
		No. of Rows=11
		No. of Columns=10
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
x[4] = 1
 Finding Variable: x[3]
	The size of Matrix is:
		No. of Rows=4
		No. of Columns=7
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=4
		No. of Columns=7
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=7
		No. of Columns=5
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	The size of Matrix is:
		No. of Rows=7
		No. of Columns=5
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	No. of New Mutants found = 0
	The size of Matrix is:
		No. of Rows=4
		No. of Columns=7
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=7
		No. of Columns=5
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	The size of Matrix is:
		No. of Rows=7
		No. of Columns=5
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	No. of New Mutants found = 0
	The size of Matrix is:
		No. of Rows=7
		No. of Columns=7
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=7
		No. of Columns=7
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
x[3] = 0
 Finding Variable: x[2]
	The size of Matrix is:
		No. of Rows=3
		No. of Columns=4
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=3
		No. of Columns=4
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=4
		No. of Columns=4
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	The size of Matrix is:
		No. of Rows=4
		No. of Columns=4
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
x[2] = 1
[0, 1, 0, 1]    



Example

Use Z/(2)[x[1..4]];
F:=[ 
    x[2]x[3] + x[1]x[4] + x[2]x[4] + x[3]x[4] + x[1] + x[2] + x[3] + x[4], 
    x[2]x[3] + x[2]x[4] + x[3]x[4] + x[2] + x[3] + x[4],  
    x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[2],  
    x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[2]
   ];

-- Solution is not unique i.e. [0, 1, 1, 1], [0, 0, 0, 0], and [1, 1, 1, 1] are solutions 

-- Then we compute the solution with
CharP.IMNLASolve(F);

-- And we achieve the following information on the screen.
----------------------------------------
    Finding Variable: x[4]
	The size of Matrix is:
		No. of Rows=4
		No. of Columns=9
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=3
		No. of Columns=9
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=9
		No. of Columns=4
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	The size of Matrix is:
		No. of Rows=9
		No. of Columns=4
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	No. of New Mutants found = 0
	The size of Matrix is:
		No. of Rows=7
		No. of Columns=14
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=14
		No. of Columns=8
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	The size of Matrix is:
		No. of Rows=14
		No. of Columns=8
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	No. of New Mutants found = 2
	The total No. of Mutants found are = 2
	The No. of Mutants of Minimum degree (Mutants used) are = 2
	The size of Matrix is:
		No. of Rows=9
		No. of Columns=10
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=10
		No. of Columns=8
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	The size of Matrix is:
		No. of Rows=10
		No. of Columns=8
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	No. of New Mutants found = 0
	The size of Matrix is:
		No. of Rows=7
		No. of Columns=10
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=10
		No. of Columns=8
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	The size of Matrix is:
		No. of Rows=10
		No. of Columns=8
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	No. of New Mutants found = 0
	The size of Matrix is:
		No. of Rows=22
		No. of Columns=14
Appling Gaussian Elimination for finding Mutants...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Compeleted.
	The size of Matrix is:
		No. of Rows=14
		No. of Columns=13
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
	The size of Matrix is:
		No. of Rows=14
		No. of Columns=13
Appling Gaussian Elimination to check solution coordinate...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
x[4] = NA
	Please Check the uniqueness of solution.
	The Given system of polynomials does not
	seem to have a unique solution or it has
	no solution over the finite field F2.


See also

CharP.MXLSolve

Introduction to CoCoAServer

Introduction to Groebner Basis in CoCoA

CharP.GBasisF2

CharP.XLSolve

CharP.IMXLSolve

CharP.MNLASolve